Traffic state estimation (TSE), a classical traffic problem, has long been studied aiming to estimate traffic states using various sensor data [1]}.
The methods that predict traffic states and characterize the robustness of the prediction can be categorized into model-based and data-driven methods.
The model-based methods assume that observed data are generated by underlying models and filtering methods can be applied to these models to propagate uncertainty.
The data-driven methods learn distributions of uncertainty directly from data without using a prior assumption of underlying physics.
The model based methods suffer from limitations such as the non-Gaussian likelihoods and high-dimensional posterior distributions [2]},
while the data-driven approaches require a huge amount of data to learn the posterior distributions from high-dimensional random inputs.
Thus, an integration of model based and data-driven methods has become a rapidly growing research arena, namely, physics-informed deep learning (PIDL) [3]}, [4]}, [5]}, [6]}.
